Considerations for Estimating Bow Shock Stand-Off Distance in (Cold Spray) Supersonic Jet Impingement

Cold spray (CS) processing often involves impingement of a supersonic, particle-laden gas jet onto an impervious substrate. Jet conditions govern kinematic and thermal histories of particles, ultimately affecting macroscopic CS outcomes such as deposition efficiency, deposit porosity, and deposit mechanical strength. Accordingly, the fluid mechanics of supersonic jet impingement (SJI) merits further investigation, in particular, to support sustained interest in computationally inexpensive 1D models approximating CS processing conditions. This work specifically focuses on time-averaged centerline bow shock standoff distance (Δ) which serves as a simple descriptor of the complex impinging jet flow field. Synthesis of physical and computational experiments conclusively demonstrates that a commonly cited correlation in cold spray literature involving Δ is quantitatively valid for the case of supersonic flow over stationary spheres, which is the situation for which this correlation was specifically developed. However, the present work shows that this correlation is quantitatively and qualitatively invalid for SJI flows relevant to CS. Dimensional reasoning applied herein indicates that Mach number M and characteristic diameter D are, alone, insufficient to predict Δ in SJI cases. Instead, dimensional reasoning suggests that, in the least, gas property and spray geometry effects must be included in the scaling, as further supported by results presented in this study.